摘要：In this paper, we investigate the existence of the nonoscillatory solutions of the following higher order neutral dynamic equation: { r n ( t ) [ ( r n − 1 ( t ) ( ⋯ ( r 1 ( t ) ( x ( t ) − q ( t ) x ( τ ( t ) ) ) Δ ) Δ ⋯ ) Δ ) Δ ] γ } Δ + f ( t , x ( δ ( t ) ) ) = 0 $\{r_{n}(t)[(r_{n-1}(t)(\cdots(r_)(t)(x(t)-q(t)x(\tau(t)))^{\Delta })^{\Delta}\cdots)^{\Delta})^{\Delta}]^{\gamma}\}^{\Delta} +f(t,x(\delta (t)))=0$ for t ∈ [ t 0 , ∞ ) T $t\in \left .[t_(,\infty) \right ._{\mathbb{T}}$ , and obtain some necessary and sufficient conditions for the existence of nonoscillatory bounded solutions for this equation.
关键词：nonoscillatory solution ; dynamic equation ; time scale
